public static void EvenDCTType3(this RealNumber[] data, ComplexNumber[] v = null)
{
int N = data.Length;
if ((N & 1) != 0)
{
throw new Exception("Inverse DCT operates only on even data sizes.");
}
N >>= 1;
Array.Resize(ref v, N);
v[0] = new ComplexNumber(data[0] + data[N], data[0] - data[N]);
//A.Conjug * B = (A * B.Conjug).Conjug
int precisionDigits = 1;
for (int i = data.Length; --i >= 0;)
{
precisionDigits = Math.Max(precisionDigits, data[i].GetPrecisionDigits());
}
RealNumber INV_SQRT_2 = new RealNumber(0.5, precisionDigits).GetSqrt();
RealNumber PI = RealNumber.GetPI(precisionDigits);
var scalej = new ComplexNumber(INV_SQRT_2, INV_SQRT_2);
ComplexNumber firstRoot = ComplexNumber.FromPolarAngle((-PI >> 2) / N);
ComplexNumber secondRoot = ComplexNumber.FromPolarAngle((-PI * 5 >> 2) / N);
ComplexNumber firstIterator = INV_SQRT_2 * firstRoot;
ComplexNumber secondIterator = INV_SQRT_2 * secondRoot.DivI();
for (int i = 1, j = N - 1; i <= j; i++, j--)
{
var a = new ComplexNumber(data[i], data[N * 2 - i]);
var b = new ComplexNumber(data[j], -data[N * 2 - j]) * scalej;
var t1 = (a + b) * firstIterator;
var t2 = (a - b) * secondIterator;
v[i] = (t1 - t2);
v[j] = (t1 + t2).Conjugate;
firstIterator *= firstRoot;
secondIterator *= secondRoot;
}
FullForwardIFFT(v, data);
for (int i = N; --i >= 0;)
{
var number = v[i];
data[map1(i * 2, N * 2)] = number.Real;
data[map1(i * 2 + 1, N * 2)] = number.Imaginary;
}
}